Years ago I found that some Seagate harddisks did no longer start spinning after turned on, because the head(s) had polished the disk surface in the landing zone, and the head(s) glued onto the disk because of this. Good candidates were ST157N or older harddisks. It turned out to be a general and well known problem.
But it seems not only to be limited to old harddisks which had a lot of start-stop-cycles, and it is of course not limited to Seagate harddisks.
In the last year I had a 105 MByte 3.5 inch SCSI harddisk from Quantum with the same problem. This disk was operated in a test computer and had indeed a lot of start-stop, at least more than 5000.
Today (2000-10-09) I found that the 80 MByte 2.5 inch Quantum GoDrive80 in my Atari ST did not spin up after 12 days off time. This is a Notebook drive which should be designed for a large number of start-stop-cycles and I know for sure that it had less than 2000 cycles in the last years in my computer.
The short term solution which does normally work is a soft strike to one of the smaller sides of the massive harddisk case. If the soft strike does not help, try a harder one. Of course, you do this ON YOUR OWN RISK! This strike usually exceeds the maximum acceleration the harddisk is guaranteed to withstand!
Unless the harddisk has some other defects, once it is spinning, it will work until you turn it off. The chance for glueing again increases with off time. Depending on harddisk and your luck, you may play the "wakeup strike game" much more than 10 times. But I recommend to backup data and replace the harddisk as soon as possible, if there is valueable data on it.
One might consider it a softer method to open the harddisk case and move the heads manually to un-glue them. Done in a clean room, this is probably true. Opening the case of the harddisk in a normally clean living room (without smoke or dust) does usually not make the harddisk immediately inoperable, but is a significant risk, too.
I personally opened a 170 MByte Fujitsu 2.5 inch IDE Notebook drive which positioned its heads beside the disks because of a defect, and after relocating the heads to the disk surface and closing the case it operated some days until it stopped with the same problem, and finally went into the trash.